Final Project

Imports

# <include-final_project/utils.py>

# <imports>
import numpy as np
import pandas as pd
import plotly.io as pio


from final_project import utils

pd.options.plotting.backend = "plotly"
pio.templates.default = "seaborn"
pio.renderers.default = "notebook_connected+vscode"

Summary

This is the exploration of a spread trading stategy involving BTCUSDT and BTCUSDT perpetual futures contracts on the binance exchange.

Overview

The basic strategy is to receive the funding rate when it is attractive and taking advantage of the fact the perptual contract and underlying asset prices converge over time as as result of the funding rate. We do this by tracking the funding rate and shorting the perpetual contract and going long the underlying asset when the funding rate is high and closing positions when the funding rate comes back down. If the funding rate goes sufficiently negative, we go long the perpetual contract and short the underlying asset.

Funding Rate

The perptual futures contract has a funding rate that are periodic payments made to either short or long traders based on the difference in the perpetual futures price and the spot price. When the market is bullish - perpetual futures price greater than the spot price - the funding rate is positive and long traders pay short traders. When it is bearish, the funding rate is negative and short traders pay long traders.

Funding rate payments are made every 8 hours starting at 00:00 UTC and only gets paid if positions are held at the designated time.

The actual rate has two components, an interest rate and a premium. The interest rate is set by the exchange and may change based on market conditions, such as changes in the federal funds rate. The current interest rate is 0.01% per eight hours, which equates to 0.03% per day or 10.8% per year. The premium is determined based on the bid ask spread relative to an index formed from a bucket of prices from major spot market exchanges need to understand better. At this point, to begin evaluating the strategy, we use the historical funding rates as provided by the exhange, and have on the todo list a fuller understanding of the mechanics of determining the funding rate.

Liquidation

Both assets are subject to automatic liquidation when collateral = initial collateral + realized and unrealized profits and losses is less than the maintenance margin. Maintenance margin is determined based on position size an leverage. Perpetual futures contracts can be traded with leverage up to 125x. need to understand better

Markets

df_exch = utils.get_exchange_info()
df_exch.loc["BTCUSDT"]

status                                                                  TRADING
baseAsset                                                                   BTC
baseAssetPrecision                                                            8
quoteAsset                                                                 USDT
quotePrecision                                                                8
quoteAssetPrecision                                                           8
baseCommissionPrecision                                                       8
quoteCommissionPrecision                                                      8
orderTypes                    [LIMIT, LIMIT_MAKER, MARKET, STOP_LOSS_LIMIT, ...
icebergAllowed                                                             True
ocoAllowed                                                                 True
quoteOrderQtyMarketAllowed                                                 True
isSpotTradingAllowed                                                       True
isMarginTradingAllowed                                                     True
filters                       [{'filterType': 'PRICE_FILTER', 'minPrice': '0...
permissions                                                      [SPOT, MARGIN]
Name: BTCUSDT, dtype: object

Perpetual Contract

tick_params = dict(
    interval="8h",
    start_time="2018-09-08"
)

df_perpetual = utils.get_continuous_contracts(pair="BTCUSDT", **tick_params)

fig = utils.make_price_volume_chart(
    df_perpetual,
    title="BTCUSDT Perpetual Contracts"
)
fig.show()

fig = utils.make_overview_chart(df_perpetual.per_return, title="BTCUSDT Perpetual", subtitle_base="Log Returns")
fig.show()

Spot Prices

These are the same prices as above.

df_spot = utils.get_klines(symbol="BTCUSDT", **tick_params)
fig = utils.make_price_volume_chart(df_spot, title="BTCUSDT Spot Price OHLC")
fig.show()

fig = utils.make_overview_chart(
    df_spot.per_return, title="BTCUSDT Spot",
    subtitle_base="Log Returns"
)
fig.show()

Funding Rate

It looks like the funding rate rarely goes negative. Is that because the perpetual price rarely goes below the spot price or is there something structural that may present and arbitrage opportunity going on?

df_funding = utils.get_funding_rate_history(symbol="BTCUSDT", start_time=tick_params["start_time"])
fig = df_funding.fundingRate.plot(title="BTCUSDT Funding Rate")
fig.update_traces(line=dict(width=1))
fig.update(layout_showlegend=False)
fig.show()

The cumulative funding rate essentially shows what return would have been generated by opening one trade short the perpetual and long the spot and holding it for the entire period.

fig = utils.make_overview_chart(
    df_funding.fundingRate, title="Funding Rate",
    subtitle_base="Funding Rate"
)
fig.show()

Spread

This is of the spread itself - the percentage difference between the perpetual and spot prices and excludes a spread outlier on 2020-12-21 of 0.018.

spread = (df_perpetual.close / df_spot.close - 1)
spread.name = "spread"
fig = utils.make_2_yaxis_lines(
    spread[spread.abs() < .015], df_funding.fundingRate,
    title="Perpetual - Spot Spread vs. Funding Rate"
)
fig.show()
# print(f"correlation: {spread[spread.abs() < .015].corr(df_funding.fundingRate):0.4f}")

fig = utils.make_overview_chart(
    spread[spread.abs() < .015],
    title="Perpetual Spot Spread",
    subtitle_base="Spread"
)
fig.show()

This shows that the difference in returns between the perpetual and the spot basically revert to zero over time, which means that there is profit to be made in chasing the funding rate, shorting the perpetual while going long the underlying asset to get the funding rate.

spread = (df_perpetual.per_return - df_spot.per_return).rolling(9).sum()
spread.name = "spread"
fig = utils.make_2_yaxis_lines(
    spread[spread.abs() < .015], df_funding.fundingRate.rolling(9).sum(),
    title="Perpetual - Spot Return Spread vs. Funding Rate"
)
# print(f"correlation: {spread[spread.abs() < .015].corr(df_funding.fundingRate):0.4f}")
fig.show()

Funding Rate Strategy

This strategy is essentially designed to capture the funding rate, shorting the perpertual and going long the underlying asset when the funding rate is high.

• Evaluates positions every 8 hours
• Trading costs assumed to be 0.05% (average of 0.03% on futures and 0.07% on the underlying asset)
• Conservatively assumes $200,000 in dedicated capital and no leverage

A better strategy would be to simply hold a short position in the perpetual and a long position in the spot and close it out much less frequently in order to avoid transaction costs.

df_ticks = utils.get_ticks(df_perpetual, df_spot, df_funding, dollar_position_size=100000)

df_ticks.head()

series	adj_close		adj_open		adj_return					position_size
asset	perpetual	spot	perpetual	spot	funding_rate	funding_rate_prior	perpetual	spot	spread	perpetual	spot
date
2019-09-10 16:00:00	10102.02	10098.15	10172.13	10176.26	0.0001	0.0001	-0.007601	-0.007588	0.000383	9.899010	9.902804
2019-09-11 00:00:00	10067.46	10066.00	10094.27	10098.19	0.0001	0.0001	-0.003427	-0.003189	0.000145	9.932992	9.934433
2019-09-11 08:00:00	9991.84	9990.07	10068.41	10066.38	0.0001	0.0001	-0.007540	-0.007572	0.000177	10.008167	10.009940
2019-09-11 16:00:00	10159.55	10158.33	9992.18	9990.57	0.0001	0.0001	0.016645	0.016702	0.000120	9.842956	9.844138
2019-09-12 00:00:00	10078.96	10079.79	10163.06	10158.75	0.0001	0.0001	-0.007964	-0.007762	-0.000082	9.921659	9.920842

df_ticks.adj_close.perpetual.shift().dropna().to_frame()

	perpetual
date
2019-09-11 00:00:00	10102.02
2019-09-11 08:00:00	10067.46
2019-09-11 16:00:00	9991.84
2019-09-12 00:00:00	10159.55
2019-09-12 08:00:00	10078.96
...	...
2021-05-31 16:00:00	36944.12
2021-06-01 00:00:00	37243.38
2021-06-01 08:00:00	36817.43
2021-06-01 16:00:00	36233.59
2021-06-02 00:00:00	36693.41

1891 rows × 1 columns

Passive Strategy

df_bench = pd.concat([
    df_ticks.adj_close.perpetual.iloc[1:] * df_ticks.adj_return.funding_rate_prior.iloc[1:],
    - df_ticks.adj_close.perpetual.diff().dropna(),
    df_ticks.adj_close.spot.diff().dropna()
], axis=1)
df_bench.columns = ["funding", "perpetual", "spot"]
df_bench["spread"] = df_bench.perpetual + df_bench.spot
df_bench["total"] = df_bench.funding + df_bench.spread
df_bench = df_bench.div(df_ticks.adj_close.perpetual.shift().dropna(), axis=0)

df_bench

	funding	perpetual	spot	spread	total
date
2019-11-28 00:00:00	0.000100	0.003541	-0.002688	0.000852	0.000952
2019-11-28 08:00:00	0.000101	-0.011844	0.011712	-0.000132	-0.000030
2019-11-28 16:00:00	0.000014	0.021459	-0.021264	0.000195	0.000209
2019-11-29 00:00:00	-0.000108	-0.013490	0.013291	-0.000199	-0.000307
2019-11-29 08:00:00	-0.000234	-0.027146	0.027146	0.000000	-0.000234
...	...	...	...	...	...
2021-05-31 16:00:00	0.000103	-0.025926	0.026032	0.000106	0.000209
2021-06-01 00:00:00	0.000098	0.019942	-0.019813	0.000129	0.000227
2021-06-01 08:00:00	0.000097	0.031968	-0.031685	0.000283	0.000380
2021-06-01 16:00:00	0.000103	-0.026118	0.025736	-0.000382	-0.000279
2021-06-02 00:00:00	0.000098	0.024235	-0.024394	-0.000159	-0.000062

1657 rows × 5 columns

fig = utils.make_overview_chart(
    df_bench.total,
    title="Passive Strategy",
    subtitle_base="8h Return"
)
fig.show()

Return would have been 53.1% on a compounded basis.

(df_bench.total + 1).prod()

1.7519258010959269

fig = utils.make_overview_chart(
    df_bench.resample("M").sum().total,
    title="Passive Strategy",
    subtitle_base="Monthly Return"
)
fig.show()

strategy_params = dict(
    pair=("spot", "perpetual"),
    df_ticks=df_ticks,
    spread_column=("adj_return", "funding_rate"),
    open_threshold=0.0005,
    close_threshold=0.0002,
    run=True,
    transact_cost_percent = 0.0005,
    closed_positions = [],
)

strategy = utils.Strategy(**strategy_params)
fig = strategy.plot()
fig.show()

df_ticks.loc["2020-05-08":].head(10)

series	adj_close		adj_open		adj_return					position_size
asset	perpetual	spot	perpetual	spot	funding_rate	funding_rate_prior	perpetual	spot	spread	perpetual	spot
date
2020-05-08 00:00:00	9818.52	9810.14	9994.74	9986.30	0.000161	0.000100	-0.017815	-0.017808	0.000854	10.184834	10.193534
2020-05-08 08:00:00	9949.28	9941.21	9818.61	9810.34	0.000340	0.000161	0.013230	0.013272	0.000812	10.050979	10.059138
2020-05-08 16:00:00	9807.49	9800.01	9949.61	9942.07	0.000532	0.000340	-0.014354	-0.014305	0.000763	10.196289	10.204071
2020-05-09 00:00:00	9609.65	9592.77	9809.63	9800.02	0.000420	0.000532	-0.020379	-0.021374	0.001760	10.406206	10.424518
2020-05-09 08:00:00	9698.04	9688.62	9608.49	9594.70	0.000758	0.000420	0.009156	0.009942	0.000972	10.311362	10.321387
2020-05-09 16:00:00	9550.67	9539.40	9697.30	9688.55	0.000580	0.000758	-0.015312	-0.015521	0.001181	10.470470	10.482840
2020-05-10 00:00:00	8807.73	8812.28	9550.25	9539.10	0.000423	0.000580	-0.080982	-0.079284	-0.000516	11.353663	11.347801
2020-05-10 08:00:00	8649.62	8650.96	8805.67	8812.27	0.000100	0.000423	-0.018114	-0.018476	-0.000155	11.561202	11.559411
2020-05-10 16:00:00	8719.53	8722.77	8649.73	8652.27	0.000100	0.000100	0.008050	0.008267	-0.000371	11.468508	11.464248
2020-05-11 00:00:00	8660.96	8664.32	8723.23	8722.77	0.000100	0.000100	-0.006740	-0.006723	-0.000388	11.546064	11.541587

Spread Strategy

Here we trade on the spread, increasing the open threshold, but it doesn't actually do much better than the funding rate only strategy, since the bulk of the profit comes from one trade on an outlier.

strategy_params = dict(
    pair=("spot", "perpetual"),
    df_ticks=df_ticks,
    spread_column=("adj_return", "spread"),
    open_threshold=0.0015,
    close_threshold=0.0002,
    run=True,
    transact_cost_percent = 0.0005,
    closed_positions = [],
)

strategy = utils.Strategy(**strategy_params)
fig = strategy.plot()
fig.show()

Spread Strategy - 1 Minute Intervals

tick_params = dict(
    interval="1m",
    start_time="2021-04-30",
    end_time="2021-05-10",
)

df_perpetual = utils.get_continuous_contracts(pair="BTCUSDT", **tick_params)
df_spot = utils.get_klines(symbol="BTCUSDT", **tick_params)

df_ticks = utils.get_ticks(df_perpetual, df_spot, df_funding, dollar_position_size=100000)

df_ticks

series	adj_close		adj_open		adj_return					position_size
asset	perpetual	spot	perpetual	spot	funding_rate	funding_rate_prior	perpetual	spot	spread	perpetual	spot
date
2021-04-30 00:01:00	53497.98	53498.26	53529.06	53529.20	0.000100	0.000100	-0.000583	-0.000578	-0.000005	1.869229	1.869220
2021-04-30 00:02:00	53486.65	53488.16	53497.98	53498.25	0.000100	0.000100	-0.000212	-0.000189	-0.000028	1.869625	1.869573
2021-04-30 00:03:00	53588.50	53583.02	53487.48	53488.16	0.000100	0.000100	0.001902	0.001772	0.000102	1.866072	1.866263
2021-04-30 00:04:00	53599.61	53585.83	53591.22	53583.03	0.000100	0.000100	0.000207	0.000052	0.000257	1.865685	1.866165
2021-04-30 00:05:00	53524.60	53509.93	53599.62	53585.83	0.000100	0.000100	-0.001400	-0.001417	0.000274	1.868300	1.868812
...	...	...	...	...	...	...	...	...	...	...	...
2021-05-09 23:56:00	58234.32	58180.19	58200.79	58143.07	0.000639	0.000639	0.000576	0.000638	0.000930	1.717200	1.718798
2021-05-09 23:57:00	58236.95	58187.90	58234.32	58180.19	0.000639	0.000639	0.000045	0.000133	0.000843	1.717123	1.718570
2021-05-09 23:58:00	58279.88	58225.32	58236.96	58187.90	0.000639	0.000639	0.000737	0.000643	0.000937	1.715858	1.717466
2021-05-09 23:59:00	58292.53	58240.84	58279.88	58225.32	0.000639	0.000639	0.000217	0.000267	0.000888	1.715486	1.717008
2021-05-10 00:00:00	58374.94	58327.60	58292.53	58240.83	0.000335	0.000639	0.001413	0.001489	0.000812	1.713064	1.714454

14400 rows × 11 columns

strategy_params = dict(
    pair=("spot", "perpetual"),
    df_ticks=df_ticks,
    spread_column=("adj_return", "spread"),
    open_threshold=0.0015,
    close_threshold=0.0002,
    run=True,
    transact_cost_percent = 0.0005,
    closed_positions = [],
)

strategy = utils.Strategy(**strategy_params)
fig = strategy.plot()
fig.show()

Funding Rate Strategy - ETH

tick_params = dict(
    interval="8h",
    start_time="2020-05-01",
)

df_perpetual = utils.get_continuous_contracts(pair="ETHUSDT", **tick_params)
df_spot = utils.get_klines(symbol="ETHUSDT", **tick_params)
df_funding = utils.get_funding_rate_history(symbol="ETHUSDT", start_time=tick_params["start_time"])

fig = utils.make_overview_chart(
    df_funding.fundingRate, title="Funding Rate",
    subtitle_base="Funding Rate"
)
fig.show()

df_ticks = utils.get_ticks(df_perpetual, df_spot, df_funding, dollar_position_size=100000)

df_ticks

series	adj_close		adj_open		adj_return					position_size
asset	perpetual	spot	perpetual	spot	funding_rate	funding_rate_prior	perpetual	spot	spread	perpetual	spot
date
2020-05-01 08:00:00	210.06	209.80	212.85	212.54	0.000196	0.000100	-0.013054	-0.013070	0.001239	476.054461	476.644423
2020-05-01 16:00:00	212.22	212.02	210.05	209.80	0.000335	0.000196	0.010230	0.010526	0.000943	471.209123	471.653618
2020-05-02 00:00:00	211.27	211.12	212.21	212.01	0.000203	0.000335	-0.004487	-0.004254	0.000710	473.327969	473.664267
2020-05-02 08:00:00	213.23	212.96	211.27	211.09	0.000288	0.000203	0.009234	0.008678	0.001268	468.977161	469.571751
2020-05-02 16:00:00	213.99	213.90	213.22	213.02	0.000655	0.000288	0.003558	0.004404	0.000421	467.311557	467.508181
...	...	...	...	...	...	...	...	...	...	...	...
2021-05-31 16:00:00	2706.33	2706.15	2637.94	2637.47	0.000100	0.000100	0.025595	0.025703	0.000067	36.950409	36.952867
2021-06-01 00:00:00	2652.36	2652.53	2706.46	2706.15	0.000100	0.000100	-0.020144	-0.020013	-0.000064	37.702273	37.699856
2021-06-01 08:00:00	2567.57	2568.49	2652.35	2652.37	0.000100	0.000100	-0.032490	-0.032196	-0.000358	38.947332	38.933381
2021-06-01 16:00:00	2634.63	2634.57	2567.57	2568.62	0.000100	0.000100	0.025783	0.025402	0.000023	37.955994	37.956858
2021-06-02 00:00:00	2606.53	2605.92	2634.61	2634.31	0.000100	0.000100	-0.010723	-0.010934	0.000234	38.365183	38.374163

1191 rows × 11 columns

strategy_params = dict(
    pair=("spot", "perpetual"),
    df_ticks=df_ticks,
    spread_column=("adj_return", "funding_rate"),
    open_threshold=0.0005,
    close_threshold=0.0001,
    run=True,
    transact_cost_percent = 0.0005,
    closed_positions = [],
)

strategy = utils.Strategy(**strategy_params)
fig = strategy.plot()
fig.show()

pd.DataFrame(strategy.stats)

	date	funding_rate_profit	position_profit	transact_cost	realized_profit	unrealized_profit	total_profit	tick_profit	total_return	tick_return
0	2020-05-01 08:00:00	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.0	0.000000	0.000000
1	2020-05-01 16:00:00	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.0	0.000000	0.000000
2	2020-05-02 00:00:00	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.0	0.000000	0.000000
3	2020-05-02 08:00:00	0.000000	0.000000	0.000000	0.000000	0.0	0.000000	0.0	0.000000	0.000000
4	2020-05-02 16:00:00	0.000000	0.000000	-100.000000	-100.000000	-100.0	-200.000000	-200.0	-0.001001	-0.001001
...	...	...	...	...	...	...	...	...	...	...
1186	2021-05-31 16:00:00	155401.342774	-61.769718	-1361.766245	153977.806812	0.0	153977.806812	0.0	0.570917	0.000000
1187	2021-06-01 00:00:00	155401.342774	-61.769718	-1361.766245	153977.806812	0.0	153977.806812	0.0	0.570917	0.000000
1188	2021-06-01 08:00:00	155401.342774	-61.769718	-1361.766245	153977.806812	0.0	153977.806812	0.0	0.570917	0.000000
1189	2021-06-01 16:00:00	155401.342774	-61.769718	-1361.766245	153977.806812	0.0	153977.806812	0.0	0.570917	0.000000
1190	2021-06-02 00:00:00	155401.342774	-61.769718	-1361.766245	153977.806812	0.0	153977.806812	0.0	0.570917	0.000000

1191 rows × 10 columns

pd.DataFrame(strategy.closed_positions)

	position_type	open_date	security	shares	open_price	open_transact_cost	close_price	close_transact_cost	closed	close_date	transact_cost_percent
0	PositionType.LONG	2020-05-02 16:00	spot	467.508181	213.90	50.0	201.23	47.038336	True	2020-05-15 00:00	0.0005
1	PositionType.SHORT	2020-05-02 16:00	perpetual	467.311557	213.99	50.0	201.09	46.985840	True	2020-05-15 00:00	0.0005
2	PositionType.LONG	2020-07-23 00:00	spot	381.010440	262.46	50.0	346.19	65.951002	True	2020-09-07 08:00	0.0005
3	PositionType.SHORT	2020-07-23 00:00	perpetual	380.633374	262.72	50.0	346.09	65.866702	True	2020-09-07 08:00	0.0005
4	PositionType.LONG	2020-10-21 16:00	spot	256.160664	390.38	50.0	2438.92	312.377683	True	2021-05-19 16:00	0.0005
5	PositionType.SHORT	2020-10-21 16:00	perpetual	255.780643	390.96	50.0	2442.98	312.433497	True	2021-05-19 16:00	0.0005
6	PositionType.LONG	2021-05-19 16:00	perpetual	40.933614	2442.98	50.0	2711.74	55.500659	True	2021-05-20 00:00	0.0005
7	PositionType.SHORT	2021-05-19 16:00	spot	41.001755	2438.92	50.0	2712.69	55.612525	True	2021-05-20 00:00	0.0005

Liquidation Price

Example

Calculate liquidation price in One-way & Cross margin mode

wallet_balance = 1535443.01

df_positions = pd.DataFrame([
    {"position": "ETHUSDT", "shares": 3683.979, "entry_price": 1456.84, "mark_price": 1335.18, "liquidation_price": 1153.25, "pnl": -447482.1, "maintenance_margin_rate": 0.10, "maintenance_amount": 135365},
    {"position": "BTCUSDT", "shares": 109.488, "entry_price": 32481.98, "mark_price": 31967.27, "liquidation_price": 26316.86, "pnl": -56248.35, "maintenance_margin_rate": .025, "maintenance_amount": 16300}
    
]).set_index("position")
df_positions

	shares	entry_price	mark_price	liquidation_price	pnl	maintenance_margin_rate	maintenance_amount
position
ETHUSDT	3683.979	1456.84	1335.18	1153.25	-447482.10	0.100	135365
BTCUSDT	109.488	32481.98	31967.27	26316.86	-56248.35	0.025	16300

notional_value = df_positions.mark_price * df_positions.shares
notional_value

position
ETHUSDT    4.918775e+06
BTCUSDT    3.500032e+06
dtype: float64

mainentance_margin = notional_value * df_positions.maintenance_margin_rate - df_positions.maintenance_amount
mainentance_margin

position
ETHUSDT    356512.508122
BTCUSDT     71200.811444
dtype: float64

numer = wallet_balance - mainentance_margin.BTCUSDT + df_positions.pnl.BTCUSDT + df_positions.maintenance_amount.ETHUSDT - 1 * df_positions.shares.abs().ETHUSDT * df_positions.entry_price.ETHUSDT
denom = df_positions.shares.abs().ETHUSDT * df_positions.maintenance_margin_rate.ETHUSDT - 1 * df_positions.shares.abs().ETHUSDT
numer, denom, numer / denom

(-3823609.117803999, -3315.5811, 1153.2244280810985)

capital = 100000
leverage = 2
long_spot = (capital / (leverage + 1)) * leverage
short_perpetual = capital-long_spot
mainentance_margin_rate = 1 / leverage * 0.50
long_spot, short_perpetual, mainentance_margin_rate

(66666.66666666667, 33333.33333333333, 0.25)

75000 / (37500 * 1.00015)

1.999700044993251

short_perpetual

33333.33333333333

spot_price = 37500
spot_shares = long_spot / spot_price
spread = 1.001
perpetual_price = spot_price * spread
perpetual_shares = - short_perpetual / perpetual_price

df_positions = pd.DataFrame([
    {"position": "perpetual", "shares": perpetual_shares, "entry_price": perpetual_price, "mark_price": 0., "liquidation_price": 0., "pnl": 0., "maintenance_margin_rate": mainentance_margin_rate, "maintenance_amount": mainentance_margin_rate * short_perpetual},
    {"position": "spot", "shares": spot_shares, "entry_price": spot_price, "mark_price": 0., "liquidation_price": 0., "pnl": 0., "maintenance_margin_rate": 0., "maintenance_amount": 0.}
    
]).set_index("position")
df_positions

	shares	entry_price	mark_price	liquidation_price	pnl	maintenance_margin_rate	maintenance_amount
position
perpetual	-0.888001	37537.5	0.0	0.0	0.0	0.25	8333.333333
spot	1.777778	37500.0	0.0	0.0	0.0	0.00	0.000000

df_positions.entry_price.perpetual - df_positions.maintenance_amount.perpetual / df_positions.shares.perpetual

46921.87499999999

df_positions.mark_price = 40000
df_positions.pnl = (df_positions.mark_price - df_positions.entry_price) * df_positions.shares
wallet_balance = (df_positions.shares * df_positions.mark_price).sum() - ((df_positions.shares * df_positions.entry_price).sum() - capital)

df_positions.maintenance_amount

position
perpetual    8333.333333
spot            0.000000
Name: maintenance_amount, dtype: float64

numer = wallet_balance + df_positions.maintenance_amount.perpetual + 1 * df_positions.shares.abs().perpetual * df_positions.entry_price.perpetual
denom = df_positions.shares.abs().perpetual * df_positions.maintenance_margin_rate.perpetual - 1 * df_positions.shares.abs().perpetual
numer, denom, numer / denom

(143924.4089244089, -0.6660006660006661, -216102.49999999994)

Buy and Hold